Phytochrome State Calculator.
Phytochrome State Calculator
Compute Pfr/Ptotal from red and far-red flux. Use for spectrum design, end-of-day far-red planning, and stretch management.
What is phytochrome?
Phytochrome is a photoreceptor protein that exists in two interconvertible forms:
- Pr (Pr): the red-absorbing form, peak absorption around 660 nm. The "inactive" form.
- Pfr (Pfr): the far-red-absorbing form, peak absorption around 730 nm. The "active" form.
Red light (660 nm) converts Pr → Pfr. Far-red light (730 nm) converts Pfr → Pr. At any given spectrum, the equilibrium ratio Pfr/(Pr+Pfr) — called φ (phi) or "phytochrome photoequilibrium" — settles based on the relative red vs. far-red flux.
The plant senses Pfr levels and responds. High Pfr = "I'm in open light" = compact growth, slow flowering. Low Pfr = "I'm shaded by other plants" = stretch toward light, accelerate flowering, prepare for reproduction.
What φ values mean for plants
| φ (Pfr/Ptotal) | Plant interpretation | Typical context |
|---|---|---|
| 0.85+ | Pure red light or red-dominant artificial | Indoor LED with no far-red supplement |
| 0.70-0.85 | Strong open-light signal — compact growth | Most indoor LED grow lights as designed |
| 0.55-0.70 | Moderate, sun-like equilibrium | Daylight, solar-replication recipes |
| 0.30-0.55 | Shade signal — stretch + reproductive triggers | Under-canopy, end-of-day far-red, shade |
| < 0.30 | Strong shade — strong stretch + flowering signal | Heavy canopy shade or end-of-day FR pulse |
Practical applications
End-of-day far-red (EOD-FR)
A 10-15 minute pulse of far-red light at the end of photoperiod (after main lights shut off) drops Pfr levels and signals "evening / shade" to the plant. Effects:
- Accelerates flowering in short-day cultivars (e.g., cannabis can finish 5-10 days earlier with proper EOD-FR)
- Increases stem elongation (useful in some cultivars; problematic in others)
- Some growers report increased terpene production with sustained EOD-FR exposure
Shade-avoidance management
Plants under canopy receive low R:FR (other leaves absorb red, transmit far-red) and respond by stretching. To suppress shade-avoidance stretch in dense plantings:
- Increase R:FR in supplemental lighting (high-red LED with minimal FR)
- Remove lower leaves to reduce canopy interception of red
- Wider plant spacing
Solar replication
Daylight has roughly R:FR = 1.1-1.2 (φ ~ 0.55-0.60) at noon, dropping toward 0.7-0.9 (φ ~ 0.40-0.50) at sunrise/sunset due to atmospheric scattering. Replicating this naturally varying R:FR across the day matches what plants evolved with.
Photoperiod manipulation
For day-length-sensitive crops (chrysanthemum, poinsettia, strawberry June-bearing, photoperiod cannabis), Pfr decay during the dark period is the actual photoperiod-sensing mechanism. Pfr converts back to Pr in darkness over hours; if dark period is too short for Pfr to drop below threshold, flowering doesn't trigger.
End-of-day far-red pulses speed Pfr decay, effectively shortening the "perceived" day length without changing photoperiod schedule.
The math
This calculator uses the simplified Mancinelli approximation:
φ = (σ_R × R) / (σ_R × R + σ_FR × FR) where: σ_R = absorption cross-section of Pr at red (~0.85) σ_FR = absorption cross-section of Pfr at far-red (~0.40) R = red flux (around 660 nm) FR = far-red flux (around 730 nm)
This is an approximation that works well for most agricultural decision-making. Research-grade plant physiology uses full action-spectrum integration (multiple wavelength bins weighted by phytochrome absorption spectra).
Note: φ depends on flux ratio, not absolute flux. Doubling both R and FR doesn't change φ. R:FR ratio is what matters.
Free under CC BY 4.0. Cite as "OAT Phytochrome State Calculator (openagriculturetechnology.com)". Math from Mancinelli (1994); cross-section values approximate.